2. [30 pts] A giant Economic consulting firm is preparing to move to Austin, hence will...

 

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2. [30 pts] A giant Economic consulting firm is preparing to move to Austin, hence will bid for a piece of land in Austin, to construct a building that will yield 3 acres of office space. Assume that the expected monthly revenue is $80 million/month (independent of location, for 3 acres office space). Moreover, expected monthly non-land costs (overhead) are $15 million/month and the expected monthly transportation costs are measured as T(x) = 5x² (where "x" is the distance to the city center) for the firm. Assume that the consulting firm faces four building options for its office space (each option yields exactly 3 acres of office space): Building One story 3-story 5-story 10-story Land Size 3 acres 1 acres 0.6 acres 0.3 acres Cost of Building $10 million /month $20 million /month $30 million /month $40 million /month Note that the bidding system only accepts bids converted on "per acre" basis, no matter how small/large the desired land is. a. If the consulting firm cannot engage in factor substitution, and has to build a one-story office building, what would be the bid-rent curve per acre? Derive the willingness to pay function and graph the corresponding bid-rent curve locating origin at the center of your graph. Label and solve for all intersection points. b. If the finance firm can engage in factor substitution, and can choose to build facility of their choice (out of the 4 options listed above), what would be the bid-rent curve per acre of land? Derive the willingness to pay functions (per acre) and graph the corresponding bid-rent curves (hint: Draw the merged/max curve) locating origin at the center of your graph. Label and solve for all intersection points. (Hint: Textbook does not have an example of this type, please see class notes.) 2. [30 pts] A giant Economic consulting firm is preparing to move to Austin, hence will bid for a piece of land in Austin, to construct a building that will yield 3 acres of office space. Assume that the expected monthly revenue is $80 million/month (independent of location, for 3 acres office space). Moreover, expected monthly non-land costs (overhead) are $15 million/month and the expected monthly transportation costs are measured as T(x) = 5x² (where "x" is the distance to the city center) for the firm. Assume that the consulting firm faces four building options for its office space (each option yields exactly 3 acres of office space): Building One story 3-story 5-story 10-story Land Size 3 acres 1 acres 0.6 acres 0.3 acres Cost of Building $10 million /month $20 million /month $30 million /month $40 million /month Note that the bidding system only accepts bids converted on "per acre" basis, no matter how small/large the desired land is. a. If the consulting firm cannot engage in factor substitution, and has to build a one-story office building, what would be the bid-rent curve per acre? Derive the willingness to pay function and graph the corresponding bid-rent curve locating origin at the center of your graph. Label and solve for all intersection points. b. If the finance firm can engage in factor substitution, and can choose to build facility of their choice (out of the 4 options listed above), what would be the bid-rent curve per acre of land? Derive the willingness to pay functions (per acre) and graph the corresponding bid-rent curves (hint: Draw the merged/max curve) locating origin at the center of your graph. Label and solve for all intersection points. (Hint: Textbook does not have an example of this type, please see class notes.)

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